Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-15T04:03:21.711Z Has data issue: false hasContentIssue false
  • English
  • Français

AN ANALYTICAL APPROACH FOR THE BREAKDOWN DISTRIBUTION OF A THIN OXIDE

Published online by Cambridge University Press:  08 April 2020

Peter C. KiesslerOpen the ORCID record for Peter C. Kiessler[Opens in a new window] and
Kanoktip Nimitkiatklai
Peter C. Kiessler
Affiliation:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA E-mail: kiesslp@clemson.edu
Kanoktip Nimitkiatklai
Affiliation:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA E-mail: kiesslp@clemson.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Dielectric breakdown in a thin oxide is presented in terms of an interacting particle system on a two-dimensional lattice. All edges in the system are initially assumed to be closed. An edge between two adjacent vertices will open according to an exponentially distributed random variable. Breakdown occurs at the time an open path connects the top layer of the lattice to the bottom layer. Using the extreme value theory, we show that the time until breakdown is asymptotically Weibull distributed.

Keywords

Weibull distributionextreme value theoryinteracting particle systemsdielectric breakdown

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021, pp. 595 - 610
Copyright
© Cambridge University Press 2020

References

1.Bingham, N.H., Goldie, C.M., & Teugels, J.L (1987). Regular variation. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
2.Çinlar, E. (1975). Introduction to stochastic processes. Englewood Cliffs: Prentice-Hall.Google Scholar
3.Degraeve, R., Roussel, P.H., Groeseneke, G., & Maes, H.E. (1996). A new anaytic model for the description of the intrinsic oxide breakdown statistics of ultra-thin oxides. Microelectronic Reliability 36: 1639–1642.CrossRefGoogle Scholar
4.Dumin, D.J. (2001). Oxide wearout, breakdown and reliability. International Journal of High Speed Electronics and Systems 11: 617–718.CrossRefGoogle Scholar
5.Dumin, D.J., Maddux, J.R., Scott, R.S., & Subramoniam, R. (1994). A model relating wearout to breakdown in thin oxides. IEEE Transactions on Electronic Devices 41: 1570–1580.CrossRefGoogle Scholar
6.Grimmett, G. (1989). Percolation. New York: Springer.CrossRefGoogle Scholar
7.Johnson, N.L., Kotz, S. & Balakrishnan, N. (1994). Continuous univariate distributions, vol. 1, 2nd ed. New York: Wiley Interscience.Google Scholar
8.Kiessler, P.C. & Nimitkiatklai, K. (2005). The lifetime of a random set. Journal of Applied Probability 42: 566–580.CrossRefGoogle Scholar
9.Leadbetter, M.R., Lindgren, G., & Rootzén, H. (1983). Extremes and related properties of random sequences and processes. New York: Springer.CrossRefGoogle Scholar
10.Ross, S. (2014). A first course in probability, 9th ed. Boston: Pearson.Google Scholar
11.Resnick, S.I. (1992). Adventures in stochastic processes. Boston: Birkhäuser.Google Scholar
12.Sahimi, M. (2003). Heterogeneous materials II: Linear transport and optical properties (interdisciplinary applied mathematics). New York: Springer.Google Scholar
13.Suñé, J., Placencia, I., Barniol, N., Farrés, E., Martín, F., & Aymerich, X. (1990). On the breakdown statistics of very thin SiO2 films. Thin Solid Films 185: 347–362.CrossRefGoogle Scholar